Dynamical local and nonlocal Casimir atomic phases

We develop an open-system dynamical theory of the Casimir interaction between coherent atomic waves and a material surface. The system, the external atomic waves, disturbs the environment, the electromagnetic field and the atomic dipole degrees of freedom, in a nonlocal manner by leaving footprints on distinct paths of the atom interferometer. This induces a nonlocal dynamical phase depending simultaneously on two distinct paths, beyond usual atom-optics methods and comparable to the local dynamical phase corrections. Nonlocal and local atomic phase coherences are thus equally important to capture the interplay between the external atomic motion and the Casimir interaction. Such dynamical phases are obtained for finite-width wave packets by developing a diagrammatic expansion of the disturbed environment quantum state.

Figure 1

Atom interferometer interacting with a conducting plate at $z=0$ during the time $T,$ with arm $k=1$ parallel to the plate (distance $z_0$) and arm $k=2$ flying away with a normal velocity $v_{\perp }.$

Figure 2

Double-path footprint left on the environment (dipole + EM field) by the external atomic state through the dipolar interaction ${\widehat{H}}_{AF}.$